On Parameterized Exponential Time Complexity

In this paper we define the notion of an f(k)-uniform parameterized exponential time scheme. We show that a problem can be solved in parameterized O(2o(f(k)) p(n)) time if and only if it has an f(k)-uniform parameterized exponential time scheme (p is a polynomial). We then illustrate how our formulation can be used to show that special instances of parameterized NPhard problems are as difficult as the general instances. For example, we show that the Planar Dominating Set problem on degree-3 graphs can be solved in O(2o( √ k) p(n)) parameterized time if and only if the general Planar Dominating Set problem can. Apart from their complexity theoretic implications, our results have some interesting algorithmic implications as well. Key words. parameterized complexity, subexponential time complexity, parameterized algorithms, exact algorithms

• Type: Conference
• Year: 2009
• Where: TAMC
• Authors: Jianer Chen, Iyad A. Kanj, Ge Xia
• Keywords: Applied Computing, Exponential Time Scheme, Parameterized Exponential Time, Planar Dominating Set, TAMC 2009